Sublogarithmic-transexponential series
Adele Padgett

TL;DR
This paper constructs a new ordered differential field of sublogarithmic-transexponential series, extending existing frameworks to include a transexponential function and its derivatives, and demonstrates its properties and closure under composition.
Contribution
It adapts the van den Dries, Macintyre, and Marker construction to build a new ordered differential field with a transexponential function, expanding the theory of transseries.
Findings
Built an ordered differential field of sublogarithmic-transexponential series.
Proved germs of $ ext{transexp}$-terms are ordered at infinity.
Established closure under composition for the constructed Hardy field.
Abstract
We adapt the construction of the field of logarithmic-exponential transseries of van den Dries, Macintyre, and Marker to build an ordered differential field of sublogarithmic-transexponential series. We use this structure to build a transexponential Hardy field closed under composition. Specifically, we prove that the germs at of -terms in a single variable are ordered, where is a language containing with new symbols for a transexponential function, its derivatives, and their compositional inverses.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Advanced Topology and Set Theory · Mathematical Dynamics and Fractals
